Experiment 1 Moving Reference Point Analysis
Dave Braun
July 22, 2019
This document is dedicated to conducting the analysis to test for evidence of the reference point shifting throughout the experiment.
Design and Predictions
Design. The design and analysis is a 2 (difficulty: harder than reference vs. easier than reference) X 2 (lagged difficulty: difficulty condition on previous block) within-subjects ANOVA on proportion selection of the reference deck.
Predictions. If the reference point moves as a function of what condition is being performed, then there should be a simple effect of lagged difficulty within the harder-than-reference condition, where selection of reference would be greater if the previous block was a harder-than-reference block rather than if it was an easier-than-reference block.
Results
Response Times
Below is the cleaned data:
d <- read.csv('../../../data/dstClean.csv')
n <- d %>%
group_by(subject) %>%
summarize(n()) %>%
nrow(.)
## code lagged difficulty
d <- d %>%
group_by(subject, block, cycle) %>%
summarize(difficulty = difficulty[1]) %>%
ungroup() %>%
mutate(lagDifficulty = lag(difficulty)) %>%
select(-difficulty) %>%
inner_join(d) %>%
mutate(trash = ifelse(block == 1 & cycle == 1, 1, 0)) %>%
filter(trash == 0) %>%
select(-trash)## Joining, by = c("subject", "block", "cycle")d <- d %>%
mutate(selRefDeck = ifelse(chosenDeckId == 'reference', 1, 0))
dThe sample size is 70.
Visualize the Results
cellMeans <- d %>%
group_by(subject, difficulty, lagDifficulty) %>%
summarize(srd = mean(selRefDeck)) %>%
group_by(difficulty, lagDifficulty) %>%
summarize(selRefDeck = mean(srd), se = sd(srd) / sqrt(n()))
cellMeanscellMeans %>%
ggplot(aes(x = difficulty, y = selRefDeck, group = lagDifficulty)) +
geom_bar(stat = 'identity', aes(fill = lagDifficulty), color = 'black', position = position_dodge(width = 0.9)) +
geom_errorbar(aes(ymin = selRefDeck - se, ymax = selRefDeck + se), position = position_dodge(width = 0.9), width = 0.5) +
theme_bw() +
xlab('Difficulty') +
ylab('Proportion Selection of Reference Deck') +
ylim(0,1) +
scale_fill_manual(name = 'Lagged Difficulty', values = c('Easier than Reference' = 'Light Grey', 'Harder than reference' = 'Black')) +
theme(strip.background = element_rect(color = 'black', fill = 'white'),
legend.position = 'top')
Statistics
Subject-wise cell means
d %>%
group_by(subject, lagDifficulty, difficulty) %>%
summarize(selRefDeck = mean(selRefDeck)) Omnibus Model
This is breaking because the factors aren’t fully between or within.
I think I’ll have to think about this one some more.
m1 <- ezANOVA(wid = subject, between = .(difficulty, lagDifficulty), dv = selRefDeck, data = d, detailed = TRUE)## Warning: Converting "subject" to factor for ANOVA.## Warning: The column supplied as the wid variable contains non-unique values
## across levels of the supplied between-Ss variables. Automatically fixing
## this by generating unique wid labels.## Warning: Data is unbalanced (unequal N per group). Make sure you specified
## a well-considered value for the type argument to ezANOVA().## Warning: Collapsing data to cell means. *IF* the requested effects are a
## subset of the full design, you must use the "within_full" argument, else
## results may be inaccurate.## Coefficient covariances computed by hccm()m1## $ANOVA
## Effect DFn DFd SSn SSd F
## 1 difficulty 1 268 1.371235e+00 23.11448 1.589874e+01
## 2 lagDifficulty 1 268 9.725838e-04 23.11448 1.127659e-02
## 3 difficulty:lagDifficulty 1 268 3.323065e-05 23.11448 3.852915e-04
## p p<.05 ges
## 1 8.623838e-05 * 5.600144e-02
## 2 9.155100e-01 4.207505e-05
## 3 9.843541e-01 1.437653e-06
##
## $`Levene's Test for Homogeneity of Variance`
## DFn DFd SSn SSd F p p<.05
## 1 3 268 0.1498109 8.262032 1.619832 0.1850754cs <- c(colnames(m1$ANOVA), 'n2p')
omni <- cbind(m1, data.frame(n2p = m1$ANOVA$SSn / (m1$ANOVA$SSn + m1$ANOVA$SSd)))
colnames(omni) <- cs
omniPlanned Comparisons
A work by Dave Braun
dab414@lehigh.edu